In silicoExperimentation of Glioma Microenvironment Development … _ … · Conventional...
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In silico Experimentation of Glioma MicroenvironmentDevelopment and Anti-tumor TherapyYu Wu1, Yao Lu1, Weiqiang Chen2, Jianping Fu2, Rong Fan1,3,4*
1 Department of Biomedical Engineering, Yale University, New Haven, Connecticut, United States of America, 2 Department of Mechanical Engineering, University of
Michigan, Ann Arbor, Michigan, United States of America, 3 Human and Translational Immunology Program, Yale University, New Haven, Connecticut, United States of
America, 4 Yale Comprehensive Cancer Center, Yale University, New Haven, Connecticut, United States of America
Abstract
Tumor cells do not develop in isolation, but co-evolve with stromal cells and tumor-associated immune cells in a tumormicroenvironment mediated by an array of soluble factors, forming a complex intercellular signaling network. Herein, wereport an unbiased, generic model to integrate prior biochemical data and the constructed brain tumor microenvironmentin silico as characterized by an intercellular signaling network comprising 5 types of cells, 15 cytokines, and 69 signalingpathways. The results show that glioma develops through three distinct phases: pre-tumor, rapid expansion, and saturation.We designed a microglia depletion therapy and observed significant benefit for virtual patients treated at the early stagesbut strikingly no therapeutic efficacy at all when therapy was given at a slightly later stage. Cytokine combination therapyexhibits more focused and enhanced therapeutic response even when microglia depletion therapy already fails. It wasfurther revealed that the optimal combination depends on the molecular profile of individual patients, suggesting the needfor patient stratification and personalized treatment. These results, obtained solely by observing the in silico dynamics of theglioma microenvironment with no fitting to experimental/clinical data, reflect many characteristics of human gliomadevelopment and imply new venues for treating tumors via selective targeting of microenvironmental components.
Citation: Wu Y, Lu Y, Chen W, Fu J, Fan R (2012) In silico Experimentation of Glioma Microenvironment Development and Anti-tumor Therapy. PLoS ComputBiol 8(2): e1002355. doi:10.1371/journal.pcbi.1002355
Editor: Greg Tucker-Kellogg, National University of Singapore, Singapore
Received July 25, 2011; Accepted December 4, 2011; Published February 2, 2012
Copyright: � 2012 Wu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricteduse, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This research was supported by the US National Cancer Institute Howard Temin Pathway to Independence Award (NIH 4R00 CA136759-02, PI: R.F.), theUS National Science Foundation (CMMI 1129611) (PI: J.F.) and partly by the Bill&Melinda Gates Foundation Grand Challenges Explorations Award (round 4 PI: R.F.).Y.W. is supported by the Anderson Postdoctoral Fellowship. The funders had no role in study design, data collection and analysis, decision to publish, orpreparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected]
Introduction
Tumor cells and stromal cells actively ‘‘talk’’ to each other via
an array of soluble signaling molecules, leading to co-evolution of
the tumor and its microenvironment [1,2,3,4,5]. This also implies
that the tumor microenvironment itself is a critical aspect of
disease mechanism and that the microenvironmental components,
including cells and soluble mediators, may represent a new set of
targets for anti-tumor therapy [3,6,7,8,9]. However, due to the
inherent heterogeneity of the tumor microenvironment and the
complexity of the cell-cell communication network, it remains
poorly understood at the systems level how these cells and their
communication network collectively shape a heterogeneous tumor
microenvironment and modulate tumorigenesis and metastasis.
Conventional approaches that examine one or two selected
pathways are incapable of fully assessing complex signaling
networks and recapitulate the dynamics of the tumor microenvi-
ronment, and often result in contradictory conclusions. Thus, a
systems approach that examines various cell types and the
associated intercellular signaling networks in the tumor microen-
vironment is highly desired.
In this work we choose to study the dynamics of glioblastoma
multiforme (GBM) development. GBM is one of the most
malignant brain tumors, with conventional therapies against
‘‘common’’ oncogenic targets usually ineffective due in part to
the high degree of tumor heterogeneity. Astrocytes, microglia, and
infiltrating immune cells actively interact with glioma and glioma
stem cells via complex intercellular signaling networks mediated by
an array of soluble signaling molecules, e.g., cytokines, growth
factors, and neuropoientins [10]. All these collectively shape a
tumor microenvironment that could be distinct from one patient
to another. Despite substantial research efforts and significant
advances in cancer therapeutics, human GBM remains the most
aggressive and lethal brain tumor in humans. In addition to inter-
tumoral and inter-patient heterogeneity, GBM also exhibits
significant intra-tumoral heterogeneity down to the single-cell
level [11,12]. First, glioma cells originate from a variety of
dynamically evolving progenitor cells [13]. It has been demon-
strated that GBM cells demarcated by the neural stem cell marker
CD133 exhibit much enhanced competencies for self-renewal and
tumor initiation [14,15]. Recent studies have also shown instances
in which CD133-negative cells were able to generate the same
outcomes [16,17,18,19]. Second, glioma cells constantly interact
with a variety of stromal cells. There is evidence that glioma cells
acquire the ability to recruit and subvert their untransformed
neighbor microglia into active collaborators to facilitate tumori-
genesis. Direct correlation has been reported between the grade of
glioma and the level of resident tumor microglia [20], suggesting
the mutual paracrine stimulation between microglial cells and
glioma cells [21,22,23,24]. Microglial cells recruited by glioma can
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promote tumor growth [25,26,27], dictated by paracrine loops
responsible for glioma initiation and progression (e.g., IL-6, IL-10,
TGF-b, prostaglandins, G-CSF, and GM-CSF, and growth factors
such as EGF, VEGF, HGF, and SCF). The crosstalk between
activated astroglial and glioma cells has also been documented,
although the mechanism of their interactions has not been full
revealed. For example, astroglial cells produce IL-1b [28,29] that
promotes cell proliferation [30,31,32] and tumor angiogenesis
[33,34,35]. Upon stimulation by the autocrine IL-1b these cells
further secrete TNF-a and IL-6 [36,37,38]. The former was found
to increase VEGF [39], EGF receptor [40], and MMP-9 [41]
expression in glioma cells, suggesting that astroglia-produced
cytokines may influence all the three most critical aspects of glioma
cell survival: angiogenesis (VEGF), proliferation (EGFR), and
migration (MMP-9).
In silico models of tumor microenvironment integrate informa-
tion about the biological context in which cancers develop, and
thus represent a multi-scale consideration of oncogenesis as it
occurs within somatic tissues [42,43]. Multiple factors involved in
the development of an intrinsically complex tumor microenviron-
ment have been studied including extracellular biomolecules, a
spatially intricate and dynamic vasculature, and the immune
system. Thus far, these models can be broadly divided into
‘continuum’ models, and discrete or ‘agent-based’ models as
summarized in a review by Price and coauthors [43]. The latter
describe the dynamics of individual interacting units, such as
cancer cells, in small confined space; the former can be applied to
a large tissue scale where agent-based modeling is computationally
prohibitive. However, none of these methods have been integrated
with a large cell-cell communication network in a complex tumor
microenvironment. Herein we integrate all the intercellular
signaling pathways known to date for human glioblastoma and
generate a dynamic cell-cell communication network associated
with the glioma microenvironment. Then we apply evolutionary
population dynamics and the Hill functions to interrogate this
intercellular signaling network and execute an in silico tumor
microenvironment development. The observed results reveal a
profound influence of the microenvironmental cues on tumor
initiation and growth, and suggest new venues for glioblastoma
treatment by targeting cells or soluble mediators in the tumor
microenvironment.
Results
Constructing the intercellular signaling network of theglioblastoma microenvironment
Although much is known about the identities and biochemical
activities of signaling molecules in the glioma microenvironment
[1,2,3,4,5,44,45], how these mediators coordinate and function
collectively at the systems level to regulate tumor development is
insufficiently understood. Here we first constructed an intercellular
signaling network by incorporating all the autocrine/paracrine
pathways known for human glioblastoma, as shown in the diagram
of Fig. 1a. Five types of cells – quiescent and activated glioma
initiating/progenitor cells, glioma cells, and astroglial and
microglial cells – and a panel of 15 growth factors/cytokines/
chemokines were included in the signaling network. Then we
derived a quantitative model using stochastic population dynamics
and the Hill functions. First, a basic population dynamic equation
was employed to compute the growth rate of five cell types as a
function of their proliferation rate, decay(apoptosis) rate, the rate
of formation via direct mutation, the rate of formation via
differentiation of their stem/progenitor cells, and the rate of de-
differentiation. Second, the temporal growth rate of each cell type
is also modulated by soluble signaling mediators present in the
tumor microenvironment; this process is quantitatively described
by the Hill functions. All differential equations are described in
Supporting Text S1 and the initial settings of all parameters are
detailed in Supporting Table S1. As an example, we present here
the procedure on how to construct the model for glioma cell
population. It has been suggested that glioma can originate from
cells at multiple differentiation stages during glial cell develop-
ment, whereas the progenitor cells appear to be more susceptible
to neoplastic transformation compared with mature glial cells
[46,47]. Cytokine signalings, including IL-1, IL-6, IL-10, TGF-b,
EGF, VEGF, HGF, G-CSF, SCF, and MIF, participate in the
mechanism of promoting GBM growth. PGE2 can transiently
prevent glioma cell proliferation in vitro. EGF, FGF, and MIF are
predominantly survival factors for GBM cells. To re-illustrate the
underlying physics of this model, we show the population
dynamics for glioma cells as in equation 1, which integrate all
the above signalings:
dcglioma
dt~fdifferentiation.H2(cFGF,cIL6){fdedifferentiation.H4(cFGF )zfmutation
zfproliferation.L(cQSC ,cASC ,cglioma ,castrocyte,cmicroglia ,Aangiogenesis)
.H3(cIL1,cIL6,cIL10,cTGFb,cEGF,cTNFa,cVEGF,cHGF,cGCSF,cSCF,cMIF,cPGE2)
{fdecay.H5(cEGF,cFGF,cMIF)
ð1Þ
where ccell/cytoine is the concentration of cell/cytokine, f is the
basal rate function, H1, H2, H3, H4, and H5 are Hill functions, L is
a logistic function, and Aangiogenesis is defined as the angiogenesis
factor. Similarly, the same algorithm was applied to derive
population dynamics equations for other cells. More details may
be found in Method and the sections 1&2 in Supporting Text S1.
The change of cytokines associated with tumor microenviron-
ment development is described as the production and consump-
tion by all the cells and modulation by other cytokines as revealed
by prior experiments. For example, glioma stem cells, glioma cells,
and microglial cells secrete substantial amounts of VEGF. MIF
and TNF-a have been observed to induce a significant dose-
dependent increase of VEGF. The dynamics of VEGF is thus
governed by a differential equation (Eq. 10) related to these cells
and soluble mediators:
Author Summary
Tumor cells do not develop in isolation, but co-evolve withstromal cells via an array of soluble mediators. Here wereport a model to integrate prior biochemical data andconstruct a glioma microenvironment in silico, whichcomprises 5 types of cells, 15 cytokines, and 69 signalingpathways. We observed a transition of the cytokinenetwork from the microenvironmentally controlled, para-crine-based regulatory mechanism to the self-sustained,autocrine-dominant malignant state. A microglia-depletiontherapy and a cytokine combination therapy were thendesigned and show significant efficacy on virtual patients.However, the optimal response depends on both the timethe therapy is given and the molecular profiles ofindividual patients, suggesting the need for informativediagnosis and personalized treatment. These results,obtained solely by observing in silico tumor dynamicswith no fitting to experimental/clinical data, reflect manycharacteristics of human glioma development and suggestnew venues for anti-tumor treatment by selectivelytargeting microenvironmental components.
ð1Þ
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dcVEGF
dt~fASCzfglioma.H(cTNFa,cMIF)zfmicroglia{fdecay ð2Þ
where f is the basal secretion/decay rate function and H is the Hill
function. In the end, the temporal rate of growth and death of each
cell population or the rate of production and decay of each cytokine
is expressed as an ODE; a set of 20 inter-coupled ODEs were
constructed to interrogate the dynamics of intercellular signaling
network in a glioma microenvironment. To capture the stochastic
nature of cell dynamics and cytokine signaling, we applied truncated
Gaussian white noise, Poisson white noise, and bounded noise to
describe the stochastic perturbation to production/regulation rate
constants, recruitment rate, and proliferation/mutation/differenti-
ation rates, respectively. Supporting Tables S1 and S2 and Methods
give a complete description of all the signaling processes and
summarize the input values for all differential equations.
Dynamics of glioma cells, glioma stem cells, astrocytes,and microglial cells
We performed an in silico stochastic study of glioma microen-
vironment development in a 1-ml control volume over a period of
12 months and observed a non-linear, synergistic co-evolution of
all five cell types (Fig. 1b–f). The dynamics of glioma cells (GC)
exhibit three distinct phases (Fig. 1b): the pre-tumor phase (1–5
months), the rapid expansion phase (6–10 months), and the
malignant phase that corresponds to semi-steady high-grade
glioblastoma (11–12 months). The starting cell populations are
astrocyte (2.86107/ml), microglia (26106/ml), and quiescent stem
cells (QSC) (16104/ml). The initial conditions only change the
quantitative timeline of the dynamics but would not affect the
general trends observed in our model that properly reflect the
dynamics of human glioma (see Supporting Fig. S2). The number
of glioma cells at t = 0 is zero, and glioma cells develop via either
neoplastic transformation of normal astrocyte or differentiation of
glioma stem cells. The initial rate constants (time = 0) are derived
from literature reports [48,49], and become gradually subjected to
the modulation by soluble factors (cytokines and growth factors).
We observed that glioma stem cells are the major cell sources for
glioma formation. At the early stage, QSCs upon stimulation are
rapidly activated into activated stem cells (ASC) via a reversible
process conferring self-renewal capability (Fig. 1c). This step
proceeds to completion within the first month. Then both QSCs
and ASCs stay at a relatively steady state over the next four
Figure 1. Stochastic population dynamics of glioma cells, glioma stem cells, astrocytes, and microglial cells. (a) Schematicrepresentation of the intercellular signaling network in GBM. The network comprises 5 types of cells and a panel of 15 cytokines. The processesinvolving cytokine or chemokine mediation are described by solid lines, while the other processes representing changes of cell states are depicted bydashed lines. A detailed description of the ODEs and parameter settings are in Supporting Text S1. (b) One-year evolution of five types of cellsshowing three distinct phases: pre-tumor phase (I), rapid expansion phase (II), and malignant phase (III). (c) Dynamics of stem cell activation. (d)Dynamics of microglia cells. (e) Temporal change of total cell concentration. (f) Snapshots of temporal progression of tumor from a 3D Monte Carlosimulation. Supporting Video S1 is the complete video showing the one-year evolution. QSC, quiescent stem-like cell. ASC, activated stem-like cell.doi:10.1371/journal.pcbi.1002355.g001
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months before ASCs further differentiate into glioma cells in a
stochastic manner. Despite the rapid lineage conversion of stem
cells occurring as early as in the first month, glioma cells remain at
a silent state with cell density way below the clinically detectable
threshold. (For all the experiments shown here, the threshold for
detecting glioma in the clinic is assumed to be 16106/ml, which is
in agreement with the data from clinical studies [50].) During the
growth of glioma cells within the space that astrocytes occupy,
astrocytes strive to maintain their abundance as well as their
functions until they are displaced by the glioma cells in the late
stage. The number of microglial cells follows a steady increase all
the way from the pre-tumor to the malignant stage, with a small
kink occurring at the onset of rapid tumor expansion (Fig. 1d).
Although no ‘‘clinical’’ signs are observed at the first phase, the
imperceptible changes occurring in the tumor microenvironment
silently accumulate tumorigenic signals and eventually result in a
switch of fitness dominance between astrocyte and glioma. The
glioma cells acquire competitive advantages and are primed to
rapid growth within a month to reach the diagnostic threshold
(,16106/ml). This unique behavior is consistent with glioblasto-
ma development observed in animal models [17]. It was assumed
that after rapid expansion glioma cells follow a typical exponential
growth mode in the next month until reaching a tumor cell
concentration (,1.56107/ml), and then gradually turn into a slow
growth phase dictated by the logistic growth model [51,52]. The
astrocyte population shrinks due to competitive selection pressure
exerted by a microenvironment unfavorable to astrocyte prolifer-
ation or favorable to astrocyte apoptosis that decreases the fitness
advantages over time and eventually causes the loss of dominance.
We examined the contribution of direct mutation of astrocyte and
the differentiation of glioma stem cells to glioma growth. We
observed that neoplastic transformation of astrocytes directly to
glioma cells does result in the formation of small numbers of
glioma cells in the pre-cancer phase, but contributes little to tumor
development in rapid growth and expansion phases (see
Supporting Fig. S1). The total cell concentration experienced a
significant expansion during the seventh month, suggesting a
density-gradient-driven potential for the glioma cells to invade
neighboring tissues (Fig. 1e). The total cell density we observed in
the tumor microenvironment is higher than that in normal tissue,
which is quantitatively consistent with the results obtained using
tissue histology examinations [53,54,55]. A three-dimensional (3D)
stochastic simulation (Fig. 1f) shows that the evolution of all the cell
types and the time course are consistent with clinical glioblastoma
development.
Cytokine dynamics and interactionCytokine dynamics also exhibit multi-stage non-linear charac-
teristics (Fig. 2a). Activated microglial cells were found to be an
important source of cytokines in the early stage, yielding a steady
increase of cytokine concentrations prior to the emergence of
tumor. These cytokines participate in the modulation of rapid
glioma cell expansion in the later stage, suggesting that microglial
cells may play an important role in tumor initiation by priming
glioma cells at very low concentrations. Glioma cells also secrete
paracrine signaling factors that promote the proliferation and
migration of microglia, and thus in turn benefit from the increase
of microglia cells that reside in the vicinity of the glioma growth
front. The normalized dynamics curves (Fig. 2b) show that 15
cytokines fall into three categories according to their time traces.
TNF-a peaks at the end of the first phase, then gradually decreases
presumably due to the consumption by glioma cells (e.g., rebind to
TNF receptors and trigger the secondary signaling cascades). IL10
and PGE2 show a monotonic increase across all the three phases.
All the other cytokines exhibit a rapid concentration increase in
the second phase and reach a quasi-steady state correlated with the
glioma population dynamics.
Therapy targeting the cells in the tumor microenvironment:microglia depletion
We first designed a novel therapy by targeting the cellular
components of the tumor microenvironment. According to cell
population dynamics (Fig. 1), microglial cells produce an array of
cytokines that often prime glioma cells to predispose them to rapid
population expansion in the sixth month, and thus function as a
tumor-promoting factor in the tumor microenvironment. There-
fore, we designed a cell-targeting therapy that eliminates
microglial cells in the tumor microenvironment.
This therapy is realized by arbitrarily increasing the apoptotic
rate of microglia by 10 times at the early, middle, and middle to
late stages with the corresponding glioma cell density at 56104/
ml, 26105/ml, or 16106/ml, respectively. To examine the
applicability of this therapy to patients with different biomolecular
background and assess the effect of inter-patient heterogeneity on
therapeutic response, three virtual patients with different profiles
of initial parameters (cytokine production rate, receptor expression
level, etc.) within the ranges reported in the literature [56]
(Supporting Table S5) were treated using the same microglia
depletion therapy at three different stages. The results are
compared as shown in Fig. 3a–c. Two interesting features were
observed in the microglia depletion therapy experiments. First, all
patients responded in a similar manner although the length of
therapeutic benefit and the recurrence time varied from one
patient to the other. Second, the efficacy strongly depends on how
early the treatment was given to the patients (Fig. 3d). All the
patients treated at the early stage when glioma cell density
(,56104/ml) is far below the threshold for clinical tumor
detection (16106/ml) showed no recurrence within the time of
simulation. Treatment given at the early to middle stage (glioma
cell density ,26105/ml) postpones the rapid tumor growth phase
by two to four months and does give the patient therapeutic
benefit. Patients treated right as the clinical sign emerges (glioma
cell density,16106/ml) did not respond at all in terms of glioma
growth rate, suggesting that tumor cells have been fully primed
and become self-sustained with no need of paracrine signaling to
drive glioma cell proliferation.
These results, obtained by unbiased integration of basic
biochemical parameters and cell signaling processes, were found
to appropriately reflect clinical and experimental observations.
Figure 2. Cytokine dynamics. (a) Change of concentrations for all 15cytokines in the microenvironment over a period of one year. (b)Normalized cytokine concentration change over a period of one year. Itshows three types of cytokine dynamics based upon the temporaltraces. TNF-a peaks at the end of phase I. IL10 and PGE2 show constantincrease regardless the growth phases of glioma cells. Other cytokinesare apparently correlated to the three-phase growth dynamics.doi:10.1371/journal.pcbi.1002355.g002
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There is a consensus that activated microglia promote glioma
growth and promotion, which is consistent with our in silico glioma
development experiments [20,39,40,41]. Recently, an animal
model study indicated that clonal cooperation between different
mutant cells can lead to tumor formation, whereas any single-cell
type alone cannot develop into tumor [57]. What is more
interesting is that the second clone, once activated by the first
clone presumably through cytokine signaling, becomes fully self-
sustained and develops into tumor without the presence of the
first clone, which is strikingly similar to the glioma-microglia
interaction observed in our model, and thus may share
commonalities in molecular and cellular mechanisms. Our study
suggests that cells in the tumor microenvironment can be good
targets for therapeutic intervention or control of tumor progres-
sion, pointing to new venues for anti-tumor drug design and
development.
Combination therapy targeting multiple cytokinesThe results of microglia-depletion therapy indicate that patients
do not show significant responses unless they are diagnosed at the
very early stage – the time when no clinically detectable tumors
have been formed. Thus, we turn to assess the possibility of
combination therapy that directly targets a number of key cytokine
signaling pathways, which is anticipated to give more focused and
potent therapeutic effects.
Due to inter-tumoral heterogeneity, the best therapeutic
regimen must be an individually tailored combination of inhibitors
that act on selected cytokines or their receptors optimized for
the patient. We performed a sensitivity analysis to assess the
tumorigenic potential of each cytokine and find the primary
targets that, once subjected to blockade or promotion, exhibit the
most effective responses in therapeutic intervention. The Methods
and section 3 in Supporting Text S1 describe the details of this
analysis. Basically, it measures the length of time taken by glioma
cells to grow from the threshold concentration (e.g., 16106/ml) to
an objective concentration (e.g., 1.56107/ml) reflecting the
survival time of a patient after the therapy is given. Twenty-nine
tests, each perturbing a cytokine production rate or a cytokine
receptor expression level, were performed to give the sensitivity
factor of each cytokine or its receptor with respect to patient
survival probability. According to the results, forced activation of a
signaling pathway with a positive sensitivity factor is expected to
promote patient survival, and vice versa. Individualized combina-
tion therapy is designed by enhancing the signaling processes of
cytokines with the largest ‘‘positive’’ sensitivity factors and
inhibiting those with the largest ‘‘negative’’ sensitivity factors. To
test this therapy, the same virtual patients (patients 1, 2, and 3) that
were randomly designed for microglia depletion experiments are
examined here to generate sensitivity factor profiles for every
patient (Fig. 4a). Next we designed a four-cytokine combination
Figure 3. Microglia depletion therapy. This therapy was given to three randomly designed virtual patients (Supporting Table S5) andadministered at different stages corresponding to glioma cell (GC) concentration ,56104/ml, 26105/ml, and 16106/ml, respectively. (a) Response ofpatient 1 to therapies given at different stages. (b) Response of patient 2 to therapies given at different stages. (c) Response of patient 3 to therapiesgiven at different stages. (d) Snapshots of a 3D simulation showing the evolution of tumor microenvironment in patient 1 in response to microgliadepletion therapy. Supporting Video S2 shows the full video.doi:10.1371/journal.pcbi.1002355.g003
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therapy (VEGF, MIF, IL6, and HGF) optimized for patient 1, and
all the patients were given the same treatment for comparison.
First, we compared single-target therapy and combination
therapy that are administered at the time of glioma cell
density,16106/ml (Fig. 4b and Supporting Fig. S3). Although
each of the four cytokines has a large negative sensitivity factor for
promoting tumorigenesis, therapies that inhibit only one of these
cytokines can hardly alter the time course of tumor progress, due
to the homeostatic robustness of the cytokine network and the
resulting intrinsic resistance to perturbation. To overcome this
issue, we further applied to virtual patient 1 a combination
treatment that simultaneously inhibits all four cytokines, and we
Figure 4. Cytokine combination therapy. This was given to the same three virtual patients (Supporting Table S5) and administered at differentstages, corresponding to glioma cell (GC) concentration ,16106/ml, 56106/ml, 16107/ml, and 26107/ml, respectively. (a) Sensitivity analyses revealthe pro-tumorigenic potential of each cytokine in the examined tumor microenvironment. Supporting Table S7 summarizes all the parameters (u1–u29), surface receptor expression level. (b) Comparison of therapeutic efficacy between single-target and combination therapies. The combinationtherapy results in a striking synergistic effect to suppress tumor progression whereas any single target treatment does not show appreciable benefit.(c) Reponses of three patients to the same combination therapy, which is tailored to give optimum response for patient 1 based upon sensitivityanalysis. (d) Snapshots showing tumor development in patient 1 with or without combination therapy. The therapy is give at a single dose when theglioma cell density reaches 16106/ml or 56106/ml. Supporting Video S3 is the complete video showing the one-year evolution.doi:10.1371/journal.pcbi.1002355.g004
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observed substantial therapeutic responses that cannot be simply
explained by the additive effect (Supporting Fig. S4). Second, the
same therapy was given to patients 2 and 3, but did not yield
positive therapeutic responses (Fig. 4c and Supporting Fig. S5);
patient 2 exhibited a modest benefit by one month and patient 3
almost did not respond at all. Figure 4d shows the results of a 3D
stochastic simulation of cell population dynamics in response to
combination therapy administered at different times. Considering
that these treatments were administered at a middle to late stage
when clinically detectable tumors had already developed, we
conclude that the combination therapy tailored to match
individual patients is more focused and can give better therapeutic
benefit even when microglia depletion therapy fails in the middle
to late stages, highlighting the critical need for molecular diagnosis
and patient stratification prior to the design of a combination
therapy that targets the tumor microenvironment.
Discussion
To the best of our knowledge, this is the first study that
attempts to integrate a variety of cells and their intercellular
signaling pathways into a cell-cell communication network and
assess how this network controls tumor initiation and progression
at the systems level. Through in silico experimentation of tumor
microenvironment development, the dynamics of cells and
cytokines correctly reflects general trends of tumorigenesis
observed experimentally or clinically [17,51,58]. We also
discovered interesting phenomena that can be seen only at the
systems level and are often masked in conventional tumor biology
studies.
First, the cell population dynamics obtained using a set of coupled
differential equations based upon population dynamics and the
Monte Carlo method yield the full time courses of all five cell types.
Although significant inter-patient heterogeneity has been observed,
the time courses of glioma microenvironment development for all
virtual patients we encountered do share common characteristics
and all exhibit three-phase non-linear evolution dynamics. For
example, all patients experience the pre-tumor phase; the mutual
paracrine stimulation between microglial cell and glioma cell results
in the continued growth of microglia. These results, obtained via in
silico experimentation without fitting or optimization to any specific
clinical or experimental data, were found to well reflect the general
mechanisms of glioma development [17,20].
Second, soluble signaling proteins, e.g. cytokines, are the key
components mediating the cell-cell communication network in a
tumor microenvironment. We successfully integrated 15 cytokines
in 69 paracrine/autocrine pathways in the cell population
dynamics model. We further examined relative weight factors
for all the paracrine/autocrine loops associated with tumor
development. This study provides new insights into tumor
microenvironment development and suggests that therapies
targeting the cytokine-mediated intercellular signaling network in
a tumor microenvironment need to be personalized.
Third, we designed a microglia depletion therapy by adding a
virtual drug in the tumor to increase the microglia apoptosis rate.
The observation from in silico experimentation indicates that this
therapy shows some efficacy only when patients are treated at
very early stages, which is consistent with the general outcomes
of anti-cancer treatment, but provides a new mechanism to
explain the therapeutic resistance observed in the clinic. The
ineffectiveness of microglia-targeted therapy in the middle to late
phases indicates the emergence of an autocrine-dominant, self-
propelled glioma proliferation. Then, we moved to look for
another therapy that directly targets multiple key cytokines to
assess the possibility of treating glioma in the middle to late
stages. It turns out a more focused combination therapy can
suppress tumor growth at the middle stage when the tumor
becomes clinically detectable and microglia-depletion therapy is
ineffective. Further study on virtual patients reveals inter-patient
heterogeneity in response to the same combination therapy, and
highlights the importance of designing therapy individually
tailored to the patient’s tumor microenvironment. While current
anti-cancer drugs mostly target tumor cells, this study indicates
the possibility and quantitatively assessed the effectiveness of new
therapies that target cellular or molecular components of the
tumor microenvironment, pointing to completely new venues for
tumor control and treatment.
In the end, a model as reported herein may serve as a tool to
integrate clinical data obtained from informative molecular
diagnosis of patients, predict the dynamics of tumor progression,
and aid the design of personalized therapy. The technologies for
such informative diagnosis are anticipated (1) to measure both
tumor cells and a variety of cells in a tumor microenvironment,
and (2) to analyze cytokine secretion profiles at the single-cell level
such that a cytokine-mediated cell-cell communication network
can be re-constructed for any individual patient. Currently, such
technologies are not yet available in the clinic, but there have been
significant research efforts in the past years that aim to develop
single-cell proteomics technologies and clinical microchips for
informative diagnosis of complex diseases including cancer
[59,60,61,62],[63]. In the future, integration of such technologies
and the model described here can turn into a powerful clinical tool
to diagnose the tumor microenvironment and the associated
intercellular signaling network in individual patients and truly
enable personalized therapy by selective targeting of the tumor
microenvironment.
Methods
AlgorithmWhile the microenvironment exerts a significant selective pressure
on the tumor, the tumor cells persistently reshape their microenvi-
ronment to synergistically support the growth and spread of the
tumor. The dynamically changing levels of signaling molecules that
rewire tumor-stromal interactions along with tumor progression will
provide insights into the mechanisms of disease development.
Assumptions and model constructionSince this work is focused on predicting tumor time course
evolution, the model is based, for simplicity, on a well-mixed
species system. Five types of cells (quiescent and activated glioma
stem/progenitor cells, glioma cells, astrocytes, and microglial
cells) and 15 growth factors/cytokines/chemokines are integrated
in this model. We assume that the species included in the model
evolve independently of species excluded from the model
(oligodendrocyte, etc.). In the end, we present the intercellular
signaling network as a set of coupled ordinary differential
equations in terms of population dynamics. The rates of change
of cells are expressed by the conversion rate, proliferation rate,
and decay rate (see Supporting Text S1).
A set of coupled stochastic ordinary differential equations
describing the co-evolution of tumor microenvironment is construct-
ed using population dynamics and stochastic dynamics. The basic
mathematical model is based on continuous logistic proliferation and
discrete event type fluctuation, and can be described as
Glioma Microenvironment and Tumor Therapy
PLoS Computational Biology | www.ploscompbiol.org 7 February 2012 | Volume 8 | Issue 2 | e1002355
dxi
dt
z}|{rate of change ofcell concentration
~XNi (t)
k~1
Ykd(t{tk)
zfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflffl{immigration, emigration,differentiation from progenitor
z
ri(t)xi 1{xi
xi maxaangiogenesis
� �P
Ncytokine
l~1P
Ncytokine
m~11z
uil(t)yl
slzyl
� �1{fimz
fimsm
smzym
� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{proliferation
{ dixiPNcytokine
n~11{ginz
ginsn
snzyn
� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{decay
zXNcell
k~1
mik(t)xkPNcytokine
p~11{hipz
hipyp
spzyp
� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{mutation, differentiation,dedifferentiation from cellxp
ð3Þ
dyj
dt
z}|{rate of change ofcytokine concentration
~
XNcell
k~1
kjk(t)xkPNcytokine
l~1P
Ncytokine
m~1P
Ncytokine
n~11z
ujl (t)yl
sl zyl
� �1{vjmz
vjmym
smzym
� �1{wjnz
wjnsn
snzyn
� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{production from cell
{ mj yjPNcytokine
p~1 1zujpyp
spzyp
� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{decay
ð4Þ
i~1,:::,Ncell
j~1,:::,Ncytokine
where the first term of the right-hand side of Eq. (3) is the stochastic
representation of discrete event–type fluctuation, including immi-
gration, emigration, and production from progenitor. Yk is the
magnitude of the kth discrete event, i.e., the number of cells
increasing (decreasing) at time point t~tk. Ni(t) denotes a non-
homogeneous Poisson counting process with arrival rate function
li(t)w0 (i.e., the number of events per unit time) and gives the
number of events that arrive in the time interval ½0,t�. The second
term indicates the logistic proliferation of cell xi with a basic rate
function ri(t), which can be up-regulated by cytokine yl and
inhibited by ym. Parameter xi max is the saturating concentration
factor, whereas aangiogenesis is the angiogenesis factor. The initial
exponential growth will slow down and the cell concentration level
xi maxaangiogenesis is approached slowly in the late time. The third
term is the decay due to natural lifespan that can be regulated by
cytokine yn. The last term describes the mutation/differentiation/
dedifferentiation from cell xk under stimulation of cytokine yp. The
first term on the right hand side of Eq. (4) quantifies the production
of cytokine yj from cell xk with basic secretion rate function kjk(t),
and the secretion is stimulated by cytokine ym and inhibited by yn.
The last term is the decay term with half-life ln 2=mj , and can be
regulated in the presence of cytokine yp.
To further assess how fluctuations in biological processes reflect the
random nature and affect the performance of the system, we introduce
the following stochastic process interpretation of the rate parameters:
ri(t)~r0i 1ze sin
2pr0i
ln 2tzbW (t)zD
� �� �, ev1 ð5Þ
mik(t)~m0ik 1ze sin
2pr0k
ln 2tzbW (t)zD
� �� �,
0ƒm0ikƒ1, 0ƒeƒ min 1,
1
m0ik
{1
! ð6Þ
kjk(t)~k0jk max 0,1zsj(t)ð Þ ð7Þ
uil(t)~u0il max 0,1zsj(t)ð Þ ð8Þ
ujl(t)~u0jl max 0,1zsj(t)ð Þ ð9Þ
ujp(t)~u0jp max 0,1zsj(t)ð Þ ð10Þ
where W(t) is a standard Wiener process, and j(t) is a zero-mean
Gaussian white noise with unit intensity. The sections 1&2 in
Supporting Text S1 give a full set of deterministic ordinary differential
equations (ODE) and detailed explanations of stochastic description.
The stochastic dynamics are studied using Monte Carlo
simulations. The corresponding time series of the species
concentration are obtained by integrating these differential
equations numerically using the fourth-order Runge-Kutta scheme
or the fifth-order Dormand-Prince method.
Model calibrationThe parameters are assigned in the range over which the model
output most closely matches experimental observation (Supporting
Table S1). Although we calibrate the model with data from the
literature, the model parameters can easily be changed to patient-
specific clinical parameters as needed.
Sensitivity analysisTo systematically evaluate the influence of each cytokine on
tumorigenesis rate, we conduct a sensitivity test, in which the
sensitivity factor of cytokine xi can be calculated as
Si:LF (x)
Lxi
����X~X0
ð11Þ
where F(x) is the objective function (e.g., tumorigenesis time, cell
density, cytokine concentration), and x0 is the local parameter
profile.
The results show marked effects of these cytokines on the
development of glioma and suggest the possibility of designing
therapeutic intervention by targeting cytokine signaling loops
(both cytokine production and receptor expression level) (Sup-
porting Fig. S6 and Table S6). The quantitative results are also
found to be context specific; the exact time for observing tumor
formation (16106 cells/ml) depends on the profile of all initial
parameters for each virtual patient (Supporting Tables S3 and S4).
The greater the difference between cytokine sensitivity factor
landscapes, the greater is the inter-patient heterogeneity. In
addition to the quantitative manifestation of inter-patient
heterogeneity, sensitivity analysis also points to a venue to identify
a cytokine profile that potentially can serve as a molecular
signature for tumor sub-classification, and thus provides a means
to stratify patients via their cytokine profiles and to design
individualized treatment.
Supporting Information
Figure S1 Contributions of ASC differentiation and asctrocyte
mutation to glioma development.
(TIF)
ð4Þ
ð3Þ
Glioma Microenvironment and Tumor Therapy
PLoS Computational Biology | www.ploscompbiol.org 8 February 2012 | Volume 8 | Issue 2 | e1002355
Figure S2 Influence of initial conditions to tumorigenesis time.
(TIF)
Figure S3 Virtual therapy of patient #3 demonstrates the
difference of therapeutic efficacy between single-targeted and
combination-targeted.
(TIF)
Figure S4 Virtual therapies of two patients demonstrate the
therapeutic efficacy of combination-targeted therapy.
(TIF)
Figure S5 Three patients are treated with the same protocol,
which is personalized according to the cytokine secretion profile of
patient #3.
(TIF)
Figure S6 Inter-patient heterogeneity was demonstrated by
sensitivity analyses.
(TIF)
Table S1 Deterministic parameters.
(DOCX)
Table S2 Stochastic parameters.
(DOCX)
Table S3 Patients parameters for Figure S5(a).
(DOCX)
Table S4 Patients parameters for Figure S5(b).
(DOCX)
Table S5 Parameter profiles of three virtual patients for Figure 3
and 4.
(DOCX)
Table S6 The x-coordinate parameter panels for Figure S5(a).
(DOCX)
Table S7 The x-coordinate parameter panels for Figure 4(a) and
Figure S5(b).
(DOCX)
Text S1 Section 1: Deterministic description of the intercellular
signaling network. Section 2: Stochastic description of rate
parameters. Section 3: Sensitivity analysis.
(PDF)
Video S1 Evolution of tumor microenvironment without
therapy.
(MPG)
Video S2 Evolution of tumor microenvironment in patient #1
in response to microglia depletion therapy administered at glioma
cell concentration 26105/ml.
(MPG)
Video S3 Evolution of tumor microenvironment in patient #1
with personalized combination therapy when the glioma cell
density reaches 16106/ml.
(MPG)
Acknowledgments
We thank Dr. Jiangbing Zhou and Dr. Kathryn Miller-Jensen for helpful
discussion.
Author Contributions
Conceived and designed the experiments: RF. Performed the experiments:
YW. Analyzed the data: YW RF YL WC JF. Wrote the paper: RF YW.
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